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The orbital displacer: Implications and applications
CHAPTER 1
The orbital displacer: Implications and applications Ian James Sparka,b, Kui Luc a
School of Science, Engineering and IT, Federation University Australia, Churchill, VIC, Australia Centre for Informatics and Applied Optimisation, Federation University Australia, Mount Helen, VIC, Australia c School of Science, Engineering and IT, Federation University Australia, Ballarat, VIC, Australia b
Contents Introduction Swept volume to total volume ratio Working volume as a function of crank angle Minimum geometrically necessary clearance volume (and maximum compression ratio) as a function of displacer geometry Valveless port timing Support of the orbiting piston and vanes Balancing of the orbital piston and vanes Sealing of the working volume Frictional losses and lubrication Combustion in orbital displacers Cooling of orbital engines Manufacturing processes and materials Conclusions Acknowledgements References
3 7 9 12 14 23 29 29 31 32 33 33 34 34 34
Introduction In 1972 the orbital engine invented by Sarich (1970, 1973) was widely publicized in Australia. As a result of this publicity two mechanical engineering students at the Gippsland Institute of Advanced Education decided to make the orbital engine the subject matter of their final year project in 1973. Since publicity indicated that Sarich was concentrating his efforts on the development of a four-stroke orbital engine, the students (Joe Rosin and Robert Sincich) and the first author decided to concentrate their efforts on the design of an orbital two-stroke engine. Positive Displacement Machines https://doi.org/10.1016/B978-0-12-816998-8.00001-7
© 2019 Elsevier Inc. All rights reserved.
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4
Positive Displacement Machines
One obvious disadvantage of the orbital displacer invented by Sarich (1970, 1973) as the basis of a two-stroke engine was that as it did not have a crankcase, crankcase compression could not be used to force the fuel/air mixture into the combustion cavity. In order to overcome this problem, the students and the author conceived the idea of turning the orbital displacer as conceived by Sarich (1970, 1973) inside out (i.e. everting it) and then combining the Sarich displacer and the everted displacer to form a hybrid orbital displacer with a much higher swept volume/total volume ratio than could be achieved by either displacer alone (Spark, Rossin, & Sincich, 1973a, 1973b, 1973c, 1973d). The initial attraction of the hybrid orbital displacer was that the normal displacer could be used to precompress the fuel/air mixture while the everted displacer could be used to produce power by means of the two-stroke cycle. It was also discovered that the orbital motion of the piston allowed great flexibility in port timing. In short, asymmetric port timing comes naturally to the orbital displacer, whereas this can only be achieved in a reciprocating displacer with considerable difficulty. See ‘Valveless port timing’ section. Further, by developing the concept of asymmetric port timing, it was found that the orbital displacer could be used as the basis of valveless pneumatic compressors and motors and hydraulic pumps and motors. It could also be used as the basis of valveless Rankine (i.e. steam) engines. A steam engine with three cut-offs for both forward and reverse is described below in ‘Valveless port timing’ section. The variants of the orbital displacer alluded to above are especially suitable as the subject matter of student projects since the students (and supervising staff ) are forced to go back to first principles and exercise their imaginations in order to solve many of the associated problems. It is not generally realized that Wankel (1963) attempted to classify all possible forms of two-stroke rotary displacers before he concentrated his development effort on the four stroke Wankel engine as we know it today. Fig. 1 shows a displacer which except for the motion of the vanes is equivalent to Sarich’s orbital displacer as shown in Fig. 2 (Sarich, 1970, 1973). Fig. 3 shows a displacer which except for the motion of the vanes is equivalent to the everted orbital displacer of Spark et al. (1973a, 1973b, 1973c, 1973d) shown in Fig. 4. In the displacers foreshadowed by Wankel the vanes both slide and rotate, whereas in the displacers of Sarich (1970, 1973) and Spark et al. (1973a, 1973b, 1973c, 1973d) the vanes execute simple harmonic motion. However, this difference in vane motion is not trivial as it greatly influences the stresses acting on the vanes and the ease with which they can be sealed.
Stationary housing
Orbiting piston
Fig. 1 Orbital displacer foreshadowed by Wankel (1963).
TDC Orbiting piston
Vane
BDC
Stationary housing
Fig. 2 Sarich orbital displacer.
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Positive Displacement Machines
Stationary core
Master vane Vane
Orbiting piston
Fig. 3 Everted orbital displacer foreshadowed by Wankel (1963).
TDC
Stationary core
BDC
Orbiting piston
Fig. 4 Everted orbital displacer with oscillating vanes.
The orbital displacer: Implications and applications
7
Fig. 5 (after Wankel, 1963) shows a displacer wherein a single vane reciprocates in a stationary external housing in a manner similar to the movement of the four vanes shown in Sarich’s orbital displacer (Fig. 2). Similarly Fig. 6 depicts a displacer where a single vane reciprocates in a stationary internal housing similar to the motion of the four vanes shown in the everted orbital displacer of Spark et al. (1973a, 1973b, 1973c, 1973d) (Fig. 4). The essential difference between the displacers foreshadowed by Wankel (1963) and those invented by Sarich (1970, 1973) and Spark et al. (1973a, 1973b, 1973c, 1973d) is that as only one vane is used in the displacers foreshadowed by Wankel (1963), the total constant working volume is divided into two variable working volumes by means of arctuate contact between the cylindrical orbiting piston and the cylindrical internal or external housings. Sarich (1970, 1973) and Spark et al. (1973a, 1973b, 1973c, 1973d) have overcome the problem of sealing the line of arctuate contact by using two or more vanes—thus making arctuate contact unnecessary.
Swept volume to total volume ratio One advantage of rotary displacers is that they do not use connecting rods. In reciprocating displacers, the “big end” of the connecting rod executes circular motion, whereas the ‘small end’ executes approximately simple
Stationary housing
Vane
Orbiting piston
Fig. 5 Orbital displacer foreshadowed by Wankel (1963).
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Positive Displacement Machines
Orbiting piston
Vane
Stationary core
Fig. 6 Everted orbital displacer foreshadowed by Wankel (1963).
harmonic motion. This complex motion must be accommodated in the housing (or crankcase) that connects the cylinders to the crankshaft main bearings. This accommodation of the connecting rods generally ensures that the total volume of a reciprocating displacer is significantly greater than that of a rotary displacer of the same displacement. This generally leads to the rotary displacer having a higher weight to displacement ratio. Everting the Sarich orbital displacer (1970, 1973) places the orbiting piston out-board of the stationary internal core. This will generally decrease the displacement to total volume ratio as the size of the orbiting piston will be increased while the displacement will be decreased. However, if the Sarich orbital displacer is combined with the everted orbital displacer to form a hybrid orbital displacer, both the inside and outside of the orbiting piston can be used. The inside of the orbiting piston forms a moving boundary of the everted orbital displacers while the outside of the orbiting piston forms a moving boundary of a Sarich orbital displacer. As a single orbiting piston is used in both the Sarich and the everted displacer, the displacement to total volume of the hybrid orbital displacer would be greater than that of either displacer alone. The Sarich and everted orbital displacers could be more or less independent. For example, one displacer could be used as a prime mover while the
The orbital displacer: Implications and applications
9
Fig. 7 Hybrid orbital displacer. Outer (Sarich) orbital displacer ¼ precompressor. Inner (everted) orbital displacer ¼ two-stroke engine.
other could be used as a pump or compressor. Alternatively, the two displacers could be connected in series to form a two-stage pneumatic motor or compressor. Alternatively, the two displacers could be connected in series so that the Sarich displacer acts as a precompressor for the everted displacer which is used as a two-stroke engine. Since the displacement of the Sarich orbital displacer must be greater than that of the everted orbital displacer, a super charging effect is inevitable. See Fig. 7.
Working volume as a function of crank angle With respect to each working volume the area of the orbiting piston effectively decreases and increases with distance from the top dead center (TDC) position for the Sarich and everted displacers, respectively. Fig. 8 shows the working volumes of the Sarich orbital displacer (Fig. 8A) and the everted orbital displacer (Fig. 8B).
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Positive Displacement Machines
b
b
BDC r θ b
TDC
Orbiting piston
r
θ
b′
Stationary core
b
TDC
f
BDC Orbiting piston
f
Stationary core
f
f b′
(A)
(B)
Fig. 8 Dimensions of working chamber of orbital displacer. (A) Sarich and (B) Everted.
In these figures the working volume is assumed to be symmetrical with respect to the TDC–BDC plane, where r is the throw of the orbital motion, b is the distance perpendicular to the direction of oscillation of the vane from the point of contact of the vane and the piston to the TDC–BDC plane, when the piston is in the TDC position, w is the width of the piston (which is perpendicular to the page), 2ϕ is the angle between the directions of oscillation of the two vanes, Vo is the minimum everted clearance volume when ϕ is 45 degrees, and θ is the clockwise rotation of the crankshaft from the TDC position. Note that the shape of the top of the piston between the vane pads does not affect the magnitude on the swept volume. The volume of the working cavity of the Sarich displacer VS is given by; θ Vs ¼ Vos + 4wr cosϕsin 2 ðb + r sin ϕcosθÞ (1) 2 where Vos is the clearance volume of the Sarich displacer, The volume of the working cavity of the everted orbital displacer is given by; θ Ve ¼ Voe + 4wr cosϕsin 2 ðb r sinϕcos θÞ (2) 2 where Voe is the clearance volume of the everted orbital displacer, The displacement of the Sarich orbital displacer Vds is the maximum Vs (when θ ¼ 180°, so sin θ2 ¼ 1, and cos θ ¼ 1), minus the minimum Vs (when θ ¼ 0°, so sin θ2 ¼ 0). Therefore: Vds ¼ 4wr cos ϕðb r sin ϕÞ
(3)
The orbital displacer: Implications and applications
11
Similarly, the displacement of the everted orbital displacer vde is Vde ¼ 4wr cos ϕðb + r sin ϕÞ
(4)
Fig. 9 shows the ratio of the instantaneous volume of the working cavity to its displacement plotted against sin 2 θ2 when ϕ is 45 degrees. The advantage of this plot is that it emphasizes nonsinusoidal variation since a sinusoidal variation will plot as a straight line. It can be seen that the volume of the working cavity of the Sarich orbital displacer increases more rapidly from the TDC position than the working volume of the everted orbital displacer. This difference can be explained in terms of the effective area of the orbiting piston decreasing and increasing from the TDC position for the Sarich displacer and the everted orbital displacer, respectively. Note that due to the cosine term the swept volume for both the Sarich and everted orbital displacers will decrease as ϕ increases. In theory, they become zero when ϕ ¼ 90 degrees. This problem can be overcome by redefining the shape of the working volume. For example, b could be replaced with b0 which is the distance between the end of each vane in contact with the piston pad at the TDC configuration for the working cavity and the axis of displacer, where the lines of oscillation of all vanes intersect. The advantage of b0 is it is indicative of the diameter of the approximately cylindrical displacer. Since b ¼ b0 tan ϕ 2t , Eqs. (3), (4) become
Fig. 9
Volume of orbital working chamber displacement
VS sin 2 θ2 :
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Positive Displacement Machines
t Vds ¼ 4wr cosϕ b0 tanϕ r sinϕ 2
(5)
and
t Vde ¼ 4wr cos ϕ b0 tan ϕ + r sinϕ (6) 2 where t is the thickness of the vane. Note that the shape of the surface of the inner housing between the leading and trailing vanes, and the shape of the crown of the orbiting piston between the vane pads does not influence the variable volume of the working cavity. However, these shapes will affect both the geometrically necessary clearance volume and the minimum geometrically necessary clearance volume.
Minimum geometrically necessary clearance volume (and maximum compression ratio) as a function of displacer geometry In orbital displacers, there is generally a clearance volume required simply to enable the orbital piston to orbit without making contact with the external housing, in the case of the Sarich displacer, or the internal core, in the case of the everted orbital displacer. First let us consider the case where the vane pads are extended until they meet on the TDC–BDC plane. In this case, the geometrically necessary clearance volume for the Sarich orbital displacer is Vos ¼ 2w br r 2 sinϕ + wr 2 ðϕ sin ϕcos ϕÞ wr 2 ð2ϕ sin2ϕÞ (7) ¼ 2w br r 2 sin ϕ + 2 For the everted orbital displacer the geometrically necessary clearance volume is; Voe ¼ 2br ð1 cosϕÞ wr 2 ð1 cos ϕÞ2 tan ϕ
(8)
The geometrically necessary clearance volume is very sensitive to the shape of the orbiting piston. In general, this clearance volume will be minimized if the area of the piston that is perpendicular to the TDC-BDC plane is maximized. Flat pads must be provided on the orbiting piston to allow the ends of the oscillating vanes to oscillate on these pads without fluid leakage. The minimum length of these pads must be the sum of the stroke of the crankshaft and the thickness of the vanes. See Fig. 10A.
BDC E
F H
TDC B
r
C
q
f f
D TDC G
G E
f
r
B
C
F
BDC
A
A
D
f
f
(A) (II)
Maximum compression ratio
Sarich 45
700
40
600
35 500
30 25
400
20
300
15
200
10 100
5 0
0 0
20
40
(B)
60
80
100
Minimum clearance volume, (mm3)
(I)
Minimum clearance volume Maximum compression ratio
Phi, (degrees)
400
45
350
40
300
35 250
30 25
200
20
150
15
100
10 50
5 0 −20
(C)
0
20
40
60
Phi, (degrees)
Fig. 10 See figure legend on next page
80
0 100
Minimum clearance volume, (mm3)
Maximum compression ratio
Everted 50
Maximum compression ratio Minimum clearance volume
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Positive Displacement Machines
The minimum geometrically necessary clearance volume for the Sarich orbital displacer Vos (see Fig. 10A I) is given by Vos_ min ¼ 2wr 2 ð1 cosϕÞ + wr 2 ðϕ sinϕcos ϕÞ wr 2 ð2ϕ sin2ϕÞ (9) 2 The minimum geometrically necessary clearance volume for the everted orbital displacer Voe (see Fig. 10A II) is given by ¼ 2wr 2 ð1 cos ϕÞ +
Voe_ min ¼ 2wr 2 ð1 sinϕÞð1 cos ϕÞ +
wr 2 ð1 cosϕ Þ2 tan ϕ
(10)
The equations above show that the geometrical necessary clearance volume can be reduced to zero if the angle ϕ between the line of oscillation of the two vanes is zero for both the Sarich displacer and the everted orbital displacer. The maximum compression ratio can be calculated by dividing the displacement by the minimum clearance volume and adding one. Fig. 10B plots the minimum clearance volume and the maximum compression ratio against the angle between the two vanes for the Sarich orbital displacer. Fig. 10C plots the minimum clearance volume and maximum compression ratio for the everted orbital displacers.
Valveless port timing It is not generally realized that the orbiting motion of the piston in an orbital displacer makes any desired (two stroke) port timing possible. Fig. 11 depicts a hybrid orbital displacer working as a double acting pump where slots are machined in the side of the piston that are parallel to the TDC/BDC line. These slots are used to open inlet ports in the side plate when the volume of the working cavity is increasing and outlet ports when the volume of the working cavity is decreasing. This pump would work equally well as a double acting hydraulic motor. Note that the displacement of the everted Fig. 10 (A) Location of minimum geometrically necessary clearance volume. (I) Sarich, (II) Everted. (B) The minimum clearance volume and the maximum compression ratio against the angle between the two vanes (Sarich). (C) The minimum clearance volume and the maximum compression ratio against the angle between the two vanes (Everted).
The orbital displacer: Implications and applications
i = inlet port o = outlet port
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Orbiting piston
TDC o i i
BDC o
Stationary internal core
o i i
o
Stationary external housing
Fig. 11 Double acting orbital pump (or motor).
displacer has been increased by decreasing the distance between the inner and outer vanes. This would increase the geometrically necessary clearance volume, but this would have little effect on the pumping of incompressible fluids. The valve action of the slotted piston is quantitatively explained in Figs 12–14. Fig. 12 depicts a slot NOPQ in the piston of an everted orbital displacer. Rotation of edge of slot Δθ in the direction of rotation of the crankshaft will cause the opening and/or closing of a corresponding port in the side plate to be delayed. Fig. 13 depicts the variation of the volume of the working cavity with crankshaft rotation past TDC.
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Positive Displacement Machines
BDC q O
F
P K
L
G E
TDC
H
J
N
M
Stationary core Q
Orbiting piston
Δq
Vane
Fig. 12 ‘Valving’ slot in orbiting piston.
Volume
ΔV
V0
q V≈V0+ΔVsin2(–) 2
q TDC
90°
BDC
270°
TDC
Fig. 13 Variation of volume of working chamber.
Fig. 14 shows the relative locations of the edges of the slot and the ports in the end plate varies with crankshaft rotation. It can be seen that the position of maximum opening of the inlet port is 90 + Δθ, whereas the duration of the port opening is determined by the position of the orbiting active edge AE of the slot relative to the stationary active edge of the corresponding port.
The orbital displacer: Implications and applications
17
X EFGH open when XAB > X4 X4
XAB = X1 + rsin(q +Dq) X4 = GH
X3
X2 X1
XCD = X3 + rsin(q +Dq) X1 = JK JKLM open when XCD < X1
q
Fig. 14 Position of edge of valving slot.
The correct angle of the edges of the slot can be easily deduced from the desired port timing. Assuming the piston is orbiting in a clockwise direction, mark the desired opening and closing angles for both the inlet and outlet ports relative to the TDC/BDC line. See Fig. 15. The chord connecting the opening and closing of the inlet port yields the required angle for the edge of the slot which opens the inlet port. Similarly, the chord connecting the opening and closing of the exhaust port yields the required angle of the other edge of the slot which opens the exhaust port. Note that the maximum distance between the circular arc and the chord gives the maximum opening of the ports if the radius of the timing diagram is the throw of the crankshaft. The slots in the end plates need to be moved sideways to get them to open at the correct crankshaft angle. Note that the depth of the orbiting piston must be at least four times the throw of the crankshaft in order to enable the orbital motion of the piston to effect valveless port timing without undesirable leakage paths. To increase the effective depth of the piston, ears can be located adjacent to the end plate. As these ears will decrease the compression ratio of the displacer, their thickness could be limited to 10% of the width of the piston. The effective depth of the orbiting piston could be further increased by interposing port plates
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Positive Displacement Machines
Outlet closes TDC = 0 Maximum 315° opening of outlet port
270°
45° Inlet opens
Outlet opens 90° 112.5° Maximum opening of inlet port
ae = Active edge of port AE = Active edge of piston ‘slot’
Orbiting piston
AE AE
ae
Inlet port
Outlet port ae
BDC = 180 Inlet closes
Fig. 15 Determination of angle of valving slots from desired timing diagram.
between the orbiting piston and the end plates. These port plates could also form slots to accommodate the edges of the sliding vanes. One advantage of separate port plates is that they only have to accommodate the minor diameter of the crank eccentric. Another advantage is that the port timing could be changed by simply replacing the port plates and the slots in the piston. Fig. 16A shows the desired pressure–volume diagram for one working volume of an orbital displacer pumping a compressible fluid. Fig. 16B shows the crank angle–volume diagram for the same displacer cavity where flow reversals are avoided. At TDC, the outlet port has just closed and the inlet port is still closed. As the crankshaft rotates to 45 degrees the volume of the working cavity increases and the pressure drops from the outlet manifold pressure to the inlet manifold pressure. At this point, the inlet port opens so that compressible fluid flows into the expanding working cavity. At 180 degrees the inlet port closes. The compressible fluid is now compressed until its pressure increases to that of the outlet manifold at 270 degrees when
The orbital displacer: Implications and applications
19
External delivery pressure
Pressure
Inlet pressure
(A)
V0
V1
Volume
V2
V3
0°
90°
112.5°
Inlet port open
Max opening at 112.5°
Δq = 22.5°
180°
270°
315°
Outlet port open
Max opening at 315° Δq = 45°
(B)
45°
360°
Fig. 16 Pressure and crank angle versus working volume for compressor.
the outlet port opens. The fluid is then pumped from the working cavity until the outlet port closes at 360 degrees. The cycle then repeats. Fig. 17 shows the shape and location of suitable inlet and outlet ports required to achieve the above cycle. The orbiting piston is in the TDC position for the working chamber shown. Fig. 18 shows one working cavity of a Rankine (steam) engine with three cut-offs for the inlet port for both forward and reverse motion. The cut-offs are 45 degrees, 90 degrees and 180 degrees. This requires three inlet ports in the end plate to effect forward (CW) rotation and three inlet ports for reverse (ACW) motion. Note that the inlet ports for reverse motion act as outlet ports for forward motion, and vice versa. Corresponding slots in the side of the orbiting piston connect the working cavity to the ports. The flow of steam to the various ports is controlled by a spool valve. In Fig. 18, the spool valve is shown in the null (zero steam flow) position.
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Positive Displacement Machines
Outlet open C
0°
Outlet
45° Inlet open
BD
18
TD
270°
C
90° 112.5°
AE
AE
AE = active edge AE AE Inlet
Fig. 17 Arrangement of valving slot and inlet and outlet ports for compressor of Fig. 16.
TDC
HP Steam Reverse
Forward
ACW
CW 0/−180 0/−90 0/−45
0/45 0/90 0/180
Condensor
Fig. 18 Arrangement of valving slot and inlet and outlet ports for Rankine (steam) engine with three forward and reverse cut-offs.
The orbital displacer: Implications and applications
21
The underlying principles for positioning the stationary ports in the end plate and the orbiting slots in the side of the piston are as follows: • Approximately rectangular ports in the end plate or opened by approximately rectangular ports in the side of the orbiting piston. • The active edges of the ports and associated slots are always parallel. • The crank angle at which the maximum opening of a port occurs is equal to the angle of the active edge to the TDC–BDC line—90 degrees. • The ratio of port opening to crank throw is 1 cos Δθ 2 where Δθ is the angular duration of the required port opening. • The slots in the orbiting piston must not intrude into the adjacent working cavities • The slots on the orbiting piston must not open the wrong ports • The latter two problems become harder to avoid as the ratio of piston throw to piston size increases. If the maximum desired port opening is close to BDC, then the edge of the piston can be used to achieve the desired port timing, so no slot is required in the side of the orbiting piston. Fig. 19 shows an orbital two-stroke engine model aircraft engine designed by Hancorne (1979) with a precompression piston which acts as a supercharger, and a power piston. The eccentric cams supporting the
IP = inlet port OP = outlet port TP = transfer port E = exhaust port PP = port plate EP = end plate CP = centre plate
EP
PP
CP
PP
PP
PP
EP
TDC
IP
TP Pre-compression piston
BDC
E
OP Power piston
OP IP
TP
BDC
Fig. 19 Orbital model aero engine. Section through TDC/BDC line.
E
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Positive Displacement Machines
two pistons are coaxial but 180 degrees out of phase. Fig. 19 is a section through the TDC–BDC line of two of the precompression cavities and two of the power cavities. Fig. 20 is a section through opposite vanes. Fig. 21 is a section through the inlet slots of the precompression piston looking towards the power piston. The inlet port opens and closes 0 degrees and 210 degrees after TDC, respectively. Fig. 22 is a section through the outlet slots of the precompression piston looking away from the power piston. The outlet port opens and closes 180 degrees and 290 degrees after TDC, respectively. Fig. 23 is a section through the transfer edge of the power piston looking away from the precompression piston. The transfer port opens and closes 150 degrees and 240 degrees after TDC, respectively. Fig. 24 is a section through the exhaust edge of the power piston looking towards the precompression piston. The exhaust port opens and closes 120 degrees and 210 degrees after TDC, respectively. Fig. 25 shows an exploded view of the precompression piston and the power piston (with ears), and the associated vanes. Fig. 26 shows an exploded view of the two-stroke engine. Note, only a quarter of the required housings and port plates are shown. The ports in the port plates are not shown.
Vane Vane Piston Piston
Piston Piston Vane Vane
Fig. 20 Orbital model aero engine. Section through vanes.
The orbital displacer: Implications and applications
23
IP= inlet port
IP
IP
IP
IP
Fig. 21 Precompression piston. Section through in inlet slots.
Note that the length and thereby the area of the inlet and outlet ports can be increased by locating them in opposing port plates. Their length can be further increased if ears on the face of the piston are used to open and close the ports.
Support of the orbiting piston and vanes In order to prevent jamming of the sliding components, it is essential that the orbital piston is prevented from rotating. This can be achieved by supporting the orbiting piston on three or more eccentrics (provided their axes do not lie in the same plane). This was the method originally used by Sarich (1970, 1973), where the piston was supported by a main crankshaft eccentric and multiple stabilizing eccentrics. As the piston tended to expand more than the end plate when the displacer was operating as an internal combustion engine, the stabilizing eccentrics tended to tighten up leading to bearing failure. To overcome this problem multiple eccentrics were used to support a
OP = outlet port Orbiting piston Stabilising plate
OP
OP
OP
OP
Fig. 22 Precompression piston. Section through outlet slots.
TP = Transfer port
Orbiting piston
TP
Stabilising plate
Fig. 23 Power piston. Section through transfer end.
The orbital displacer: Implications and applications
25
EP = Exhaust port
EP
EP
EP
EP
Fig. 24 Power Piston. Section through Exhaust end.
stabilizing plate where a tongue on the stabilizing plate engaged a groove in the orbiting piston. This system enabled the piston to expand radially without increasing the load on the eccentric bearings. The orbital motion was enforced by a main crankshaft eccentric (Sarich, 1975, 1976a). Alternatively, the orbiting piston can be supported by a single crankshaft eccentric combined with a stabilizing plate based on an Oldham coupling. See Fig. 27. This plate is imposed between one end plate and the side of the adjacent orbital piston. Tongues on one side of the plate slidably engage with slots in the end plate. These slots could be continuations of the grooves that slidably engage the vane legs. The other side of the stabilizing plate has tongues, which are aligned at right angles to the tongues that slidably engage the groove in the end plate. The former tongues slidably engage with slots in the end of the piston. This arrangement enables the stabilizing plate to execute simple harmonic motion (SHM) relative to the end plate, and the piston to execute simply harmonic motion relative to the stabilizing plate. These two SHMs can add to allow the piston to orbit around a circular path, while
26
Positive Displacement Machines
Fig. 25 Precompression and power pistons.
preventing its rotation. The stabilizing plate must contain an elongated hole to allow it to oscillate relative to the crankshaft. The side of the piston must contain a recess that enables the stabilizing plate to oscillate relative to the piston. The orbiting pistons of everted and hybrid displacers could best be supported by multiple eccentrics. If the eccentrics are connected by means of an idler gear, then only two eccentrics would be required. The idler gear could be used to deliver or extract power from the orbiting piston. It could also be used for speed reduction of the power input or output. Three or more unconnected eccentrics could be used as shown in Fig. 28. The vanes can be forced to execute SHM by slidably connecting them to the orbiting piston by means of lugs on the ends of the vane legs which slide in grooves in the sides of the orbiting piston (which are at right angles to the direction of oscillation of the vanes). The vane legs slide in groves in the end plates and are attached to the vane proper in the course of assembling the displacer.
The orbital displacer: Implications and applications
Fig. 26 Exploded view of orbital model aero engine.
27
Fig. 27 Piston stabilizing plate based on Oldham coupling.
E
T2
T2
T3
T3
T1
E
E
Fig. 28 Orbital two-stroke engine with three precompression and three power chambers.
The orbital displacer: Implications and applications
29
One of the factors that distinguishes the Sarich orbital engine from other less successful vane engines is that the vanes of the orbital engine are positively supported on three of their four edges—as opposed to being cantilevered from slots in the housing. Supporting opposite edges of the vanes in grooves in the end plates is possible because the vanes only execute SHM relative to these end plates. In the case of the hybrid displacer, the vanes and vane legs encompass the hybrid orbital piston, thus making grooves in the sides of the piston unnecessary. See Figs 7 and 11. The crankshaft and stabilizing eccentrics can be balanced by traditional methods.
Balancing of the orbital piston and vanes One advantage of the orbital engine is that there is no secondary out of balance. Static and dynamic balance can be easily achieved by means of adding counter weights at both ends of the crankshaft. The question arises as to how the reciprocating vanes can be balanced. If the direction of reciprocation is uniformly distributed around the crankshaft, and all the vanes have identical mass, then the reciprocation of all the vanes is equivalent to rotation of a mass equal to half the mass of the vanes. Hence, for the purpose of balancing the vanes, half their mass should be added to the mass of the associated piston, in order to deduce the mass and location of the counter weights required to produce static and dynamic balance of the displacer. When the lines of action of the vanes exhibit less than three-fold symmetry, either dummy vanes can be added to restore the necessary axial symmetry, or balance weights on a counter-rotating shaft can be used. Note that the stabilizing plate generally oscillates in common with two diametrically opposite vanes. In this case the stabilizing plate can be balanced by adjusting the weight of the associated vanes so that the weight of each of these vanes plus half the weight of the stabilizing plate is the same as the weight of a standard vane. Indeed, the stabilizing plate could be attached to the vane leg that slides in the same groove.
Sealing of the working volume Whereas the working volume of a reciprocating displacer is bounded by two surfaces, the working volume of the orbital displacer is bounded by four surfaces. These are the stationary housing or core (and end plates), the face of the orbiting piston and the sides of two vanes. The piston orbits relative to
30
Positive Displacement Machines
the stationary housing or core (and end plates). The vanes execute SHM relative to both the stationary housing or core (and end plates), and the orbiting piston. Effective sealing must be achieved between the following sliding couples: The piston sides and the end plates, the piston faces and the end of the vanes; the vane legs and the grooves in the end plates; the side of the vanes and slots in the housing or core; the inner face of the vane leg and the side of the piston. Sarich (1974, 1976b) has proposed a suitable sealing system. An exploded view of an alternative suitable sealing system is shown in Fig. 29. Fig. 30 shows a section through the centre of an assembled vane. In this case the seals are rectangular prisms pushed against their mating surface by wave springs. It is anticipated that sealing of a 6.0 cc model aircraft engine shown above will be less of a problem since effective sealing can be achieved by lapping together interacting components, and then maintaining the resultant small clearances by balancing the thermal expansion of these components. It should be noted that many model aircraft engines of comparable displacement run without the benefit of piston rings. Since the orientation of the components that move relative to one another, remains constant, they will tend to make contact over an area rather
Fig. 29 Exploded view of sealing possible system.
The orbital displacer: Implications and applications
31
WS = wave spring SE = sealing element
Vane leg
Key
WS WS SE
SE
WS
SE
Piston
Fig. 30 Sealing system. Section through centre of vane.
than along a line, thus reducing the compressive stresses acting in the contact zone.
Frictional losses and lubrication Since the piston orbits but does not rotate, all positions on the piston describe a circle whose radius is the throw of the crank. Consequently, rubbing speeds are much lower than in rotary engines where the piston also rotates, such as the Wankel engine. These low rubbing speeds lead to low frictional losses of power. There appear to be no lubrication problems unique to the orbital displacer where pressurized oil systems can be used. Since “crankcase compression” is not used in the orbital two-stroke engines cited above, a total loss oil system (with its “sooty” exhaust) is not required.
32
Positive Displacement Machines
Combustion in orbital displacers Although it is difficult to design an orbital displacer where the ratio of the surface area of the working cavity to the displacement is as low as that of a reciprocating internal combustion engine, this ratio will generally be much lower than that pertaining to the Wankel engine. Note that the centre of the working volume moves in a roughly elliptical orbit, whereas it moves straight up and down in a reciprocating engine. This should cause an inherent swirl of the fuel/air mixture which could be used to facilitate combustion. See Fig. 31. Furthermore, if the clearance between the crown of the piston and the housing is minimized, a very high gas velocity across the piston crown can be achieved. Just before TDC most of the working volume is located adjacent to the leading vane. Just after TDC most of the working volume is located adjacent to the trailing vane. See Fig. 32. If a shallow groove in the piston crown links the leading vane pad to the trailing vain pad, most of the fuel/air mixture will be forced to flow through this groove around TDC. If one or more spark plugs were located in the housing above this groove, all the fuel/
Fig. 31 Schematic of swirl in orbital power chamber.
Fig. 32 Squish in orbital power chamber.
The orbital displacer: Implications and applications
33
air mixture could be squirted past these discharging spark plugs around TDC—thus making the combustion process less dependent on the rate of flame propagation.
Cooling of orbital engines In the (single rotor) Wankel engine, the combustion chambers travel past a single inlet port, single sparkplug and single exhaust port. In this case, the heat flow to the housing is nonuniform, thus complicating the thermal expansion and cooling problems. In an orbital engine, the combustion chambers tend to be uniformly distributed around the axis of their crankshaft. In general, if there are N vanes there will be N combustion chambers, each with its own sparkplug and inlet and exhaust ports. In this case, the heat flow to the housing should show radial symmetry, thus simplifying the thermal expansion and cooling problems. Since the orbiting piston will generally float between the end plates and does not touch the housing, its cooling is a potential problem. A similar problem occurs in the Wankel engine. Forced convection will be required to cool the orbiting piston. In small engines air circulation may suffice, whereas in larger engines oil cooling of the piston may be required. Cooling holes could be drilled through the piston parallel to the axes of the eccentrics, which intermittently align with cooling holes in the end plates. Air could be drawn through these holes by a fan attached to one or more of the eccentrics. Alternatively, oil could be pumped through much smaller holes through the orbiting piston.
Manufacturing processes and materials In theory, the cost of manufacturing an orbital displacer could be less than that pertaining to a reciprocating displacer. First, with the exception of the sealing elements, there are fewer components required—especially in the case of orbital pumps and motors, where valveless port timing can be used to eliminate the need for valves. Furthermore, little machining is required. In the external housing or internal core, only the vane slots and end faces need to be machined. On the end plates, only the inner faces, the grooves for the vanes, and the bores for the crankshaft need to be machined. On the piston, only the end faces, the pads for the vanes, and the eccentric bore need to be machined. Most
34
Positive Displacement Machines
surfaces of the vanes will need to be machined, as will the crankshaft eccentric and stabilizing plate. The 6 cc model aircraft engine was designed to be manufactured from an Al-17% Si alloy which combines lightness with wear resistance.
Conclusions The orbital displacer originally conceived by Ralph Sarich may have greater significance than its application as a four-stroke internal combustion engine. Although the automobile engine market is very large, it is also the hardest to penetrate due to the high degree of sophistication of the design and manufacture of reciprocating engines and the large number of often conflicting requirements that must be satisfied. It may be more rewarding to first penetrate a smaller, less competitive market and then use this as a base from which to expand into larger more difficult markets. Asymmetric port timing comes naturally to orbital displacers. This valveless port timing can be used to advantage in orbital two-stroke engines, hydraulic pumps and motors, pneumatic compressors and motors, and Rankine engines. Engineering students have found orbital displacer projects stimulating in the originality required, as they generally had to go back to first principles to solve problems.
Acknowledgements The authors would like to thank the staff and students of the Gippsland School of Engineering (now part of Federation University Australia) for their contribution to this paper.
References Hancorne, J. A. (1979). Student project report. Gippsland Institute of Advanced Education. Private Communication. Sarich, T. R. (1970). An improved rotary motor. Australian patent 467415, filing date 6 July 1970. Sarich, T. R. (1973). Improved vane type internal combustion engines. Australian patent 477125, filing date 16 January 1973. Sarich, T. R. (1974). Gas seal for vane type internal combustion engine. (US patent 3938916, filing date 16 January 1974). Sarich, T. R. (1975). Improved orbital engine with stabilising plate. In Australian patent 491267, filing date 3 February 1975. Sarich, T. R. (1976a). Orbital engine with stabilizing plate. US patent 4037997, filing date 3 February 1976a.
The orbital displacer: Implications and applications
35
Sarich, T. R. (1976b). Vane type orbital engine. US patent 4079083, filing date 3 February 1976b. Spark, I. J., Rossin, J. M., & Sincich, R. (1973a). Improved orbital displacers. Australian patent 487540, filing date 2 July 1973. Spark, I. J., Rossin, J. M., & Sincich, R. (1973b). Orbital displacer. US patent 487540, filing date 2 July 1973. Spark, I. J., Rossin, J. M., & Sincich, R. (1973c). Improvements in rotary positive-displacement machines. UK patent 1480137, filing date 2 July 1973. Spark, I. J., Rossin, J. M., & Sincich, R. (1973d). Orbital displacers. Canadian patent 1043267, filing date 2 July 1973. Wankel, F. (1963). Rotary piston machines. London: Iliffe Books.
The orbital displacer: Implications and applications Ian James Sparka,b, Kui Luc a
School of Science, Engineering and IT, Federation University Australia, Churchill, VIC, Australia Centre for Informatics and Applied Optimisation, Federation University Australia, Mount Helen, VIC, Australia c School of Science, Engineering and IT, Federation University Australia, Ballarat, VIC, Australia b
Contents Introduction Swept volume to total volume ratio Working volume as a function of crank angle Minimum geometrically necessary clearance volume (and maximum compression ratio) as a function of displacer geometry Valveless port timing Support of the orbiting piston and vanes Balancing of the orbital piston and vanes Sealing of the working volume Frictional losses and lubrication Combustion in orbital displacers Cooling of orbital engines Manufacturing processes and materials Conclusions Acknowledgements References
3 7 9 12 14 23 29 29 31 32 33 33 34 34 34
Introduction In 1972 the orbital engine invented by Sarich (1970, 1973) was widely publicized in Australia. As a result of this publicity two mechanical engineering students at the Gippsland Institute of Advanced Education decided to make the orbital engine the subject matter of their final year project in 1973. Since publicity indicated that Sarich was concentrating his efforts on the development of a four-stroke orbital engine, the students (Joe Rosin and Robert Sincich) and the first author decided to concentrate their efforts on the design of an orbital two-stroke engine. Positive Displacement Machines https://doi.org/10.1016/B978-0-12-816998-8.00001-7
© 2019 Elsevier Inc. All rights reserved.
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4
Positive Displacement Machines
One obvious disadvantage of the orbital displacer invented by Sarich (1970, 1973) as the basis of a two-stroke engine was that as it did not have a crankcase, crankcase compression could not be used to force the fuel/air mixture into the combustion cavity. In order to overcome this problem, the students and the author conceived the idea of turning the orbital displacer as conceived by Sarich (1970, 1973) inside out (i.e. everting it) and then combining the Sarich displacer and the everted displacer to form a hybrid orbital displacer with a much higher swept volume/total volume ratio than could be achieved by either displacer alone (Spark, Rossin, & Sincich, 1973a, 1973b, 1973c, 1973d). The initial attraction of the hybrid orbital displacer was that the normal displacer could be used to precompress the fuel/air mixture while the everted displacer could be used to produce power by means of the two-stroke cycle. It was also discovered that the orbital motion of the piston allowed great flexibility in port timing. In short, asymmetric port timing comes naturally to the orbital displacer, whereas this can only be achieved in a reciprocating displacer with considerable difficulty. See ‘Valveless port timing’ section. Further, by developing the concept of asymmetric port timing, it was found that the orbital displacer could be used as the basis of valveless pneumatic compressors and motors and hydraulic pumps and motors. It could also be used as the basis of valveless Rankine (i.e. steam) engines. A steam engine with three cut-offs for both forward and reverse is described below in ‘Valveless port timing’ section. The variants of the orbital displacer alluded to above are especially suitable as the subject matter of student projects since the students (and supervising staff ) are forced to go back to first principles and exercise their imaginations in order to solve many of the associated problems. It is not generally realized that Wankel (1963) attempted to classify all possible forms of two-stroke rotary displacers before he concentrated his development effort on the four stroke Wankel engine as we know it today. Fig. 1 shows a displacer which except for the motion of the vanes is equivalent to Sarich’s orbital displacer as shown in Fig. 2 (Sarich, 1970, 1973). Fig. 3 shows a displacer which except for the motion of the vanes is equivalent to the everted orbital displacer of Spark et al. (1973a, 1973b, 1973c, 1973d) shown in Fig. 4. In the displacers foreshadowed by Wankel the vanes both slide and rotate, whereas in the displacers of Sarich (1970, 1973) and Spark et al. (1973a, 1973b, 1973c, 1973d) the vanes execute simple harmonic motion. However, this difference in vane motion is not trivial as it greatly influences the stresses acting on the vanes and the ease with which they can be sealed.
Stationary housing
Orbiting piston
Fig. 1 Orbital displacer foreshadowed by Wankel (1963).
TDC Orbiting piston
Vane
BDC
Stationary housing
Fig. 2 Sarich orbital displacer.
6
Positive Displacement Machines
Stationary core
Master vane Vane
Orbiting piston
Fig. 3 Everted orbital displacer foreshadowed by Wankel (1963).
TDC
Stationary core
BDC
Orbiting piston
Fig. 4 Everted orbital displacer with oscillating vanes.
The orbital displacer: Implications and applications
7
Fig. 5 (after Wankel, 1963) shows a displacer wherein a single vane reciprocates in a stationary external housing in a manner similar to the movement of the four vanes shown in Sarich’s orbital displacer (Fig. 2). Similarly Fig. 6 depicts a displacer where a single vane reciprocates in a stationary internal housing similar to the motion of the four vanes shown in the everted orbital displacer of Spark et al. (1973a, 1973b, 1973c, 1973d) (Fig. 4). The essential difference between the displacers foreshadowed by Wankel (1963) and those invented by Sarich (1970, 1973) and Spark et al. (1973a, 1973b, 1973c, 1973d) is that as only one vane is used in the displacers foreshadowed by Wankel (1963), the total constant working volume is divided into two variable working volumes by means of arctuate contact between the cylindrical orbiting piston and the cylindrical internal or external housings. Sarich (1970, 1973) and Spark et al. (1973a, 1973b, 1973c, 1973d) have overcome the problem of sealing the line of arctuate contact by using two or more vanes—thus making arctuate contact unnecessary.
Swept volume to total volume ratio One advantage of rotary displacers is that they do not use connecting rods. In reciprocating displacers, the “big end” of the connecting rod executes circular motion, whereas the ‘small end’ executes approximately simple
Stationary housing
Vane
Orbiting piston
Fig. 5 Orbital displacer foreshadowed by Wankel (1963).
8
Positive Displacement Machines
Orbiting piston
Vane
Stationary core
Fig. 6 Everted orbital displacer foreshadowed by Wankel (1963).
harmonic motion. This complex motion must be accommodated in the housing (or crankcase) that connects the cylinders to the crankshaft main bearings. This accommodation of the connecting rods generally ensures that the total volume of a reciprocating displacer is significantly greater than that of a rotary displacer of the same displacement. This generally leads to the rotary displacer having a higher weight to displacement ratio. Everting the Sarich orbital displacer (1970, 1973) places the orbiting piston out-board of the stationary internal core. This will generally decrease the displacement to total volume ratio as the size of the orbiting piston will be increased while the displacement will be decreased. However, if the Sarich orbital displacer is combined with the everted orbital displacer to form a hybrid orbital displacer, both the inside and outside of the orbiting piston can be used. The inside of the orbiting piston forms a moving boundary of the everted orbital displacers while the outside of the orbiting piston forms a moving boundary of a Sarich orbital displacer. As a single orbiting piston is used in both the Sarich and the everted displacer, the displacement to total volume of the hybrid orbital displacer would be greater than that of either displacer alone. The Sarich and everted orbital displacers could be more or less independent. For example, one displacer could be used as a prime mover while the
The orbital displacer: Implications and applications
9
Fig. 7 Hybrid orbital displacer. Outer (Sarich) orbital displacer ¼ precompressor. Inner (everted) orbital displacer ¼ two-stroke engine.
other could be used as a pump or compressor. Alternatively, the two displacers could be connected in series to form a two-stage pneumatic motor or compressor. Alternatively, the two displacers could be connected in series so that the Sarich displacer acts as a precompressor for the everted displacer which is used as a two-stroke engine. Since the displacement of the Sarich orbital displacer must be greater than that of the everted orbital displacer, a super charging effect is inevitable. See Fig. 7.
Working volume as a function of crank angle With respect to each working volume the area of the orbiting piston effectively decreases and increases with distance from the top dead center (TDC) position for the Sarich and everted displacers, respectively. Fig. 8 shows the working volumes of the Sarich orbital displacer (Fig. 8A) and the everted orbital displacer (Fig. 8B).
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Positive Displacement Machines
b
b
BDC r θ b
TDC
Orbiting piston
r
θ
b′
Stationary core
b
TDC
f
BDC Orbiting piston
f
Stationary core
f
f b′
(A)
(B)
Fig. 8 Dimensions of working chamber of orbital displacer. (A) Sarich and (B) Everted.
In these figures the working volume is assumed to be symmetrical with respect to the TDC–BDC plane, where r is the throw of the orbital motion, b is the distance perpendicular to the direction of oscillation of the vane from the point of contact of the vane and the piston to the TDC–BDC plane, when the piston is in the TDC position, w is the width of the piston (which is perpendicular to the page), 2ϕ is the angle between the directions of oscillation of the two vanes, Vo is the minimum everted clearance volume when ϕ is 45 degrees, and θ is the clockwise rotation of the crankshaft from the TDC position. Note that the shape of the top of the piston between the vane pads does not affect the magnitude on the swept volume. The volume of the working cavity of the Sarich displacer VS is given by; θ Vs ¼ Vos + 4wr cosϕsin 2 ðb + r sin ϕcosθÞ (1) 2 where Vos is the clearance volume of the Sarich displacer, The volume of the working cavity of the everted orbital displacer is given by; θ Ve ¼ Voe + 4wr cosϕsin 2 ðb r sinϕcos θÞ (2) 2 where Voe is the clearance volume of the everted orbital displacer, The displacement of the Sarich orbital displacer Vds is the maximum Vs (when θ ¼ 180°, so sin θ2 ¼ 1, and cos θ ¼ 1), minus the minimum Vs (when θ ¼ 0°, so sin θ2 ¼ 0). Therefore: Vds ¼ 4wr cos ϕðb r sin ϕÞ
(3)
The orbital displacer: Implications and applications
11
Similarly, the displacement of the everted orbital displacer vde is Vde ¼ 4wr cos ϕðb + r sin ϕÞ
(4)
Fig. 9 shows the ratio of the instantaneous volume of the working cavity to its displacement plotted against sin 2 θ2 when ϕ is 45 degrees. The advantage of this plot is that it emphasizes nonsinusoidal variation since a sinusoidal variation will plot as a straight line. It can be seen that the volume of the working cavity of the Sarich orbital displacer increases more rapidly from the TDC position than the working volume of the everted orbital displacer. This difference can be explained in terms of the effective area of the orbiting piston decreasing and increasing from the TDC position for the Sarich displacer and the everted orbital displacer, respectively. Note that due to the cosine term the swept volume for both the Sarich and everted orbital displacers will decrease as ϕ increases. In theory, they become zero when ϕ ¼ 90 degrees. This problem can be overcome by redefining the shape of the working volume. For example, b could be replaced with b0 which is the distance between the end of each vane in contact with the piston pad at the TDC configuration for the working cavity and the axis of displacer, where the lines of oscillation of all vanes intersect. The advantage of b0 is it is indicative of the diameter of the approximately cylindrical displacer. Since b ¼ b0 tan ϕ 2t , Eqs. (3), (4) become
Fig. 9
Volume of orbital working chamber displacement
VS sin 2 θ2 :
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Positive Displacement Machines
t Vds ¼ 4wr cosϕ b0 tanϕ r sinϕ 2
(5)
and
t Vde ¼ 4wr cos ϕ b0 tan ϕ + r sinϕ (6) 2 where t is the thickness of the vane. Note that the shape of the surface of the inner housing between the leading and trailing vanes, and the shape of the crown of the orbiting piston between the vane pads does not influence the variable volume of the working cavity. However, these shapes will affect both the geometrically necessary clearance volume and the minimum geometrically necessary clearance volume.
Minimum geometrically necessary clearance volume (and maximum compression ratio) as a function of displacer geometry In orbital displacers, there is generally a clearance volume required simply to enable the orbital piston to orbit without making contact with the external housing, in the case of the Sarich displacer, or the internal core, in the case of the everted orbital displacer. First let us consider the case where the vane pads are extended until they meet on the TDC–BDC plane. In this case, the geometrically necessary clearance volume for the Sarich orbital displacer is Vos ¼ 2w br r 2 sinϕ + wr 2 ðϕ sin ϕcos ϕÞ wr 2 ð2ϕ sin2ϕÞ (7) ¼ 2w br r 2 sin ϕ + 2 For the everted orbital displacer the geometrically necessary clearance volume is; Voe ¼ 2br ð1 cosϕÞ wr 2 ð1 cos ϕÞ2 tan ϕ
(8)
The geometrically necessary clearance volume is very sensitive to the shape of the orbiting piston. In general, this clearance volume will be minimized if the area of the piston that is perpendicular to the TDC-BDC plane is maximized. Flat pads must be provided on the orbiting piston to allow the ends of the oscillating vanes to oscillate on these pads without fluid leakage. The minimum length of these pads must be the sum of the stroke of the crankshaft and the thickness of the vanes. See Fig. 10A.
BDC E
F H
TDC B
r
C
q
f f
D TDC G
G E
f
r
B
C
F
BDC
A
A
D
f
f
(A) (II)
Maximum compression ratio
Sarich 45
700
40
600
35 500
30 25
400
20
300
15
200
10 100
5 0
0 0
20
40
(B)
60
80
100
Minimum clearance volume, (mm3)
(I)
Minimum clearance volume Maximum compression ratio
Phi, (degrees)
400
45
350
40
300
35 250
30 25
200
20
150
15
100
10 50
5 0 −20
(C)
0
20
40
60
Phi, (degrees)
Fig. 10 See figure legend on next page
80
0 100
Minimum clearance volume, (mm3)
Maximum compression ratio
Everted 50
Maximum compression ratio Minimum clearance volume
14
Positive Displacement Machines
The minimum geometrically necessary clearance volume for the Sarich orbital displacer Vos (see Fig. 10A I) is given by Vos_ min ¼ 2wr 2 ð1 cosϕÞ + wr 2 ðϕ sinϕcos ϕÞ wr 2 ð2ϕ sin2ϕÞ (9) 2 The minimum geometrically necessary clearance volume for the everted orbital displacer Voe (see Fig. 10A II) is given by ¼ 2wr 2 ð1 cos ϕÞ +
Voe_ min ¼ 2wr 2 ð1 sinϕÞð1 cos ϕÞ +
wr 2 ð1 cosϕ Þ2 tan ϕ
(10)
The equations above show that the geometrical necessary clearance volume can be reduced to zero if the angle ϕ between the line of oscillation of the two vanes is zero for both the Sarich displacer and the everted orbital displacer. The maximum compression ratio can be calculated by dividing the displacement by the minimum clearance volume and adding one. Fig. 10B plots the minimum clearance volume and the maximum compression ratio against the angle between the two vanes for the Sarich orbital displacer. Fig. 10C plots the minimum clearance volume and maximum compression ratio for the everted orbital displacers.
Valveless port timing It is not generally realized that the orbiting motion of the piston in an orbital displacer makes any desired (two stroke) port timing possible. Fig. 11 depicts a hybrid orbital displacer working as a double acting pump where slots are machined in the side of the piston that are parallel to the TDC/BDC line. These slots are used to open inlet ports in the side plate when the volume of the working cavity is increasing and outlet ports when the volume of the working cavity is decreasing. This pump would work equally well as a double acting hydraulic motor. Note that the displacement of the everted Fig. 10 (A) Location of minimum geometrically necessary clearance volume. (I) Sarich, (II) Everted. (B) The minimum clearance volume and the maximum compression ratio against the angle between the two vanes (Sarich). (C) The minimum clearance volume and the maximum compression ratio against the angle between the two vanes (Everted).
The orbital displacer: Implications and applications
i = inlet port o = outlet port
15
Orbiting piston
TDC o i i
BDC o
Stationary internal core
o i i
o
Stationary external housing
Fig. 11 Double acting orbital pump (or motor).
displacer has been increased by decreasing the distance between the inner and outer vanes. This would increase the geometrically necessary clearance volume, but this would have little effect on the pumping of incompressible fluids. The valve action of the slotted piston is quantitatively explained in Figs 12–14. Fig. 12 depicts a slot NOPQ in the piston of an everted orbital displacer. Rotation of edge of slot Δθ in the direction of rotation of the crankshaft will cause the opening and/or closing of a corresponding port in the side plate to be delayed. Fig. 13 depicts the variation of the volume of the working cavity with crankshaft rotation past TDC.
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Positive Displacement Machines
BDC q O
F
P K
L
G E
TDC
H
J
N
M
Stationary core Q
Orbiting piston
Δq
Vane
Fig. 12 ‘Valving’ slot in orbiting piston.
Volume
ΔV
V0
q V≈V0+ΔVsin2(–) 2
q TDC
90°
BDC
270°
TDC
Fig. 13 Variation of volume of working chamber.
Fig. 14 shows the relative locations of the edges of the slot and the ports in the end plate varies with crankshaft rotation. It can be seen that the position of maximum opening of the inlet port is 90 + Δθ, whereas the duration of the port opening is determined by the position of the orbiting active edge AE of the slot relative to the stationary active edge of the corresponding port.
The orbital displacer: Implications and applications
17
X EFGH open when XAB > X4 X4
XAB = X1 + rsin(q +Dq) X4 = GH
X3
X2 X1
XCD = X3 + rsin(q +Dq) X1 = JK JKLM open when XCD < X1
q
Fig. 14 Position of edge of valving slot.
The correct angle of the edges of the slot can be easily deduced from the desired port timing. Assuming the piston is orbiting in a clockwise direction, mark the desired opening and closing angles for both the inlet and outlet ports relative to the TDC/BDC line. See Fig. 15. The chord connecting the opening and closing of the inlet port yields the required angle for the edge of the slot which opens the inlet port. Similarly, the chord connecting the opening and closing of the exhaust port yields the required angle of the other edge of the slot which opens the exhaust port. Note that the maximum distance between the circular arc and the chord gives the maximum opening of the ports if the radius of the timing diagram is the throw of the crankshaft. The slots in the end plates need to be moved sideways to get them to open at the correct crankshaft angle. Note that the depth of the orbiting piston must be at least four times the throw of the crankshaft in order to enable the orbital motion of the piston to effect valveless port timing without undesirable leakage paths. To increase the effective depth of the piston, ears can be located adjacent to the end plate. As these ears will decrease the compression ratio of the displacer, their thickness could be limited to 10% of the width of the piston. The effective depth of the orbiting piston could be further increased by interposing port plates
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Positive Displacement Machines
Outlet closes TDC = 0 Maximum 315° opening of outlet port
270°
45° Inlet opens
Outlet opens 90° 112.5° Maximum opening of inlet port
ae = Active edge of port AE = Active edge of piston ‘slot’
Orbiting piston
AE AE
ae
Inlet port
Outlet port ae
BDC = 180 Inlet closes
Fig. 15 Determination of angle of valving slots from desired timing diagram.
between the orbiting piston and the end plates. These port plates could also form slots to accommodate the edges of the sliding vanes. One advantage of separate port plates is that they only have to accommodate the minor diameter of the crank eccentric. Another advantage is that the port timing could be changed by simply replacing the port plates and the slots in the piston. Fig. 16A shows the desired pressure–volume diagram for one working volume of an orbital displacer pumping a compressible fluid. Fig. 16B shows the crank angle–volume diagram for the same displacer cavity where flow reversals are avoided. At TDC, the outlet port has just closed and the inlet port is still closed. As the crankshaft rotates to 45 degrees the volume of the working cavity increases and the pressure drops from the outlet manifold pressure to the inlet manifold pressure. At this point, the inlet port opens so that compressible fluid flows into the expanding working cavity. At 180 degrees the inlet port closes. The compressible fluid is now compressed until its pressure increases to that of the outlet manifold at 270 degrees when
The orbital displacer: Implications and applications
19
External delivery pressure
Pressure
Inlet pressure
(A)
V0
V1
Volume
V2
V3
0°
90°
112.5°
Inlet port open
Max opening at 112.5°
Δq = 22.5°
180°
270°
315°
Outlet port open
Max opening at 315° Δq = 45°
(B)
45°
360°
Fig. 16 Pressure and crank angle versus working volume for compressor.
the outlet port opens. The fluid is then pumped from the working cavity until the outlet port closes at 360 degrees. The cycle then repeats. Fig. 17 shows the shape and location of suitable inlet and outlet ports required to achieve the above cycle. The orbiting piston is in the TDC position for the working chamber shown. Fig. 18 shows one working cavity of a Rankine (steam) engine with three cut-offs for the inlet port for both forward and reverse motion. The cut-offs are 45 degrees, 90 degrees and 180 degrees. This requires three inlet ports in the end plate to effect forward (CW) rotation and three inlet ports for reverse (ACW) motion. Note that the inlet ports for reverse motion act as outlet ports for forward motion, and vice versa. Corresponding slots in the side of the orbiting piston connect the working cavity to the ports. The flow of steam to the various ports is controlled by a spool valve. In Fig. 18, the spool valve is shown in the null (zero steam flow) position.
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Positive Displacement Machines
Outlet open C
0°
Outlet
45° Inlet open
BD
18
TD
270°
C
90° 112.5°
AE
AE
AE = active edge AE AE Inlet
Fig. 17 Arrangement of valving slot and inlet and outlet ports for compressor of Fig. 16.
TDC
HP Steam Reverse
Forward
ACW
CW 0/−180 0/−90 0/−45
0/45 0/90 0/180
Condensor
Fig. 18 Arrangement of valving slot and inlet and outlet ports for Rankine (steam) engine with three forward and reverse cut-offs.
The orbital displacer: Implications and applications
21
The underlying principles for positioning the stationary ports in the end plate and the orbiting slots in the side of the piston are as follows: • Approximately rectangular ports in the end plate or opened by approximately rectangular ports in the side of the orbiting piston. • The active edges of the ports and associated slots are always parallel. • The crank angle at which the maximum opening of a port occurs is equal to the angle of the active edge to the TDC–BDC line—90 degrees. • The ratio of port opening to crank throw is 1 cos Δθ 2 where Δθ is the angular duration of the required port opening. • The slots in the orbiting piston must not intrude into the adjacent working cavities • The slots on the orbiting piston must not open the wrong ports • The latter two problems become harder to avoid as the ratio of piston throw to piston size increases. If the maximum desired port opening is close to BDC, then the edge of the piston can be used to achieve the desired port timing, so no slot is required in the side of the orbiting piston. Fig. 19 shows an orbital two-stroke engine model aircraft engine designed by Hancorne (1979) with a precompression piston which acts as a supercharger, and a power piston. The eccentric cams supporting the
IP = inlet port OP = outlet port TP = transfer port E = exhaust port PP = port plate EP = end plate CP = centre plate
EP
PP
CP
PP
PP
PP
EP
TDC
IP
TP Pre-compression piston
BDC
E
OP Power piston
OP IP
TP
BDC
Fig. 19 Orbital model aero engine. Section through TDC/BDC line.
E
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Positive Displacement Machines
two pistons are coaxial but 180 degrees out of phase. Fig. 19 is a section through the TDC–BDC line of two of the precompression cavities and two of the power cavities. Fig. 20 is a section through opposite vanes. Fig. 21 is a section through the inlet slots of the precompression piston looking towards the power piston. The inlet port opens and closes 0 degrees and 210 degrees after TDC, respectively. Fig. 22 is a section through the outlet slots of the precompression piston looking away from the power piston. The outlet port opens and closes 180 degrees and 290 degrees after TDC, respectively. Fig. 23 is a section through the transfer edge of the power piston looking away from the precompression piston. The transfer port opens and closes 150 degrees and 240 degrees after TDC, respectively. Fig. 24 is a section through the exhaust edge of the power piston looking towards the precompression piston. The exhaust port opens and closes 120 degrees and 210 degrees after TDC, respectively. Fig. 25 shows an exploded view of the precompression piston and the power piston (with ears), and the associated vanes. Fig. 26 shows an exploded view of the two-stroke engine. Note, only a quarter of the required housings and port plates are shown. The ports in the port plates are not shown.
Vane Vane Piston Piston
Piston Piston Vane Vane
Fig. 20 Orbital model aero engine. Section through vanes.
The orbital displacer: Implications and applications
23
IP= inlet port
IP
IP
IP
IP
Fig. 21 Precompression piston. Section through in inlet slots.
Note that the length and thereby the area of the inlet and outlet ports can be increased by locating them in opposing port plates. Their length can be further increased if ears on the face of the piston are used to open and close the ports.
Support of the orbiting piston and vanes In order to prevent jamming of the sliding components, it is essential that the orbital piston is prevented from rotating. This can be achieved by supporting the orbiting piston on three or more eccentrics (provided their axes do not lie in the same plane). This was the method originally used by Sarich (1970, 1973), where the piston was supported by a main crankshaft eccentric and multiple stabilizing eccentrics. As the piston tended to expand more than the end plate when the displacer was operating as an internal combustion engine, the stabilizing eccentrics tended to tighten up leading to bearing failure. To overcome this problem multiple eccentrics were used to support a
OP = outlet port Orbiting piston Stabilising plate
OP
OP
OP
OP
Fig. 22 Precompression piston. Section through outlet slots.
TP = Transfer port
Orbiting piston
TP
Stabilising plate
Fig. 23 Power piston. Section through transfer end.
The orbital displacer: Implications and applications
25
EP = Exhaust port
EP
EP
EP
EP
Fig. 24 Power Piston. Section through Exhaust end.
stabilizing plate where a tongue on the stabilizing plate engaged a groove in the orbiting piston. This system enabled the piston to expand radially without increasing the load on the eccentric bearings. The orbital motion was enforced by a main crankshaft eccentric (Sarich, 1975, 1976a). Alternatively, the orbiting piston can be supported by a single crankshaft eccentric combined with a stabilizing plate based on an Oldham coupling. See Fig. 27. This plate is imposed between one end plate and the side of the adjacent orbital piston. Tongues on one side of the plate slidably engage with slots in the end plate. These slots could be continuations of the grooves that slidably engage the vane legs. The other side of the stabilizing plate has tongues, which are aligned at right angles to the tongues that slidably engage the groove in the end plate. The former tongues slidably engage with slots in the end of the piston. This arrangement enables the stabilizing plate to execute simple harmonic motion (SHM) relative to the end plate, and the piston to execute simply harmonic motion relative to the stabilizing plate. These two SHMs can add to allow the piston to orbit around a circular path, while
26
Positive Displacement Machines
Fig. 25 Precompression and power pistons.
preventing its rotation. The stabilizing plate must contain an elongated hole to allow it to oscillate relative to the crankshaft. The side of the piston must contain a recess that enables the stabilizing plate to oscillate relative to the piston. The orbiting pistons of everted and hybrid displacers could best be supported by multiple eccentrics. If the eccentrics are connected by means of an idler gear, then only two eccentrics would be required. The idler gear could be used to deliver or extract power from the orbiting piston. It could also be used for speed reduction of the power input or output. Three or more unconnected eccentrics could be used as shown in Fig. 28. The vanes can be forced to execute SHM by slidably connecting them to the orbiting piston by means of lugs on the ends of the vane legs which slide in grooves in the sides of the orbiting piston (which are at right angles to the direction of oscillation of the vanes). The vane legs slide in groves in the end plates and are attached to the vane proper in the course of assembling the displacer.
The orbital displacer: Implications and applications
Fig. 26 Exploded view of orbital model aero engine.
27
Fig. 27 Piston stabilizing plate based on Oldham coupling.
E
T2
T2
T3
T3
T1
E
E
Fig. 28 Orbital two-stroke engine with three precompression and three power chambers.
The orbital displacer: Implications and applications
29
One of the factors that distinguishes the Sarich orbital engine from other less successful vane engines is that the vanes of the orbital engine are positively supported on three of their four edges—as opposed to being cantilevered from slots in the housing. Supporting opposite edges of the vanes in grooves in the end plates is possible because the vanes only execute SHM relative to these end plates. In the case of the hybrid displacer, the vanes and vane legs encompass the hybrid orbital piston, thus making grooves in the sides of the piston unnecessary. See Figs 7 and 11. The crankshaft and stabilizing eccentrics can be balanced by traditional methods.
Balancing of the orbital piston and vanes One advantage of the orbital engine is that there is no secondary out of balance. Static and dynamic balance can be easily achieved by means of adding counter weights at both ends of the crankshaft. The question arises as to how the reciprocating vanes can be balanced. If the direction of reciprocation is uniformly distributed around the crankshaft, and all the vanes have identical mass, then the reciprocation of all the vanes is equivalent to rotation of a mass equal to half the mass of the vanes. Hence, for the purpose of balancing the vanes, half their mass should be added to the mass of the associated piston, in order to deduce the mass and location of the counter weights required to produce static and dynamic balance of the displacer. When the lines of action of the vanes exhibit less than three-fold symmetry, either dummy vanes can be added to restore the necessary axial symmetry, or balance weights on a counter-rotating shaft can be used. Note that the stabilizing plate generally oscillates in common with two diametrically opposite vanes. In this case the stabilizing plate can be balanced by adjusting the weight of the associated vanes so that the weight of each of these vanes plus half the weight of the stabilizing plate is the same as the weight of a standard vane. Indeed, the stabilizing plate could be attached to the vane leg that slides in the same groove.
Sealing of the working volume Whereas the working volume of a reciprocating displacer is bounded by two surfaces, the working volume of the orbital displacer is bounded by four surfaces. These are the stationary housing or core (and end plates), the face of the orbiting piston and the sides of two vanes. The piston orbits relative to
30
Positive Displacement Machines
the stationary housing or core (and end plates). The vanes execute SHM relative to both the stationary housing or core (and end plates), and the orbiting piston. Effective sealing must be achieved between the following sliding couples: The piston sides and the end plates, the piston faces and the end of the vanes; the vane legs and the grooves in the end plates; the side of the vanes and slots in the housing or core; the inner face of the vane leg and the side of the piston. Sarich (1974, 1976b) has proposed a suitable sealing system. An exploded view of an alternative suitable sealing system is shown in Fig. 29. Fig. 30 shows a section through the centre of an assembled vane. In this case the seals are rectangular prisms pushed against their mating surface by wave springs. It is anticipated that sealing of a 6.0 cc model aircraft engine shown above will be less of a problem since effective sealing can be achieved by lapping together interacting components, and then maintaining the resultant small clearances by balancing the thermal expansion of these components. It should be noted that many model aircraft engines of comparable displacement run without the benefit of piston rings. Since the orientation of the components that move relative to one another, remains constant, they will tend to make contact over an area rather
Fig. 29 Exploded view of sealing possible system.
The orbital displacer: Implications and applications
31
WS = wave spring SE = sealing element
Vane leg
Key
WS WS SE
SE
WS
SE
Piston
Fig. 30 Sealing system. Section through centre of vane.
than along a line, thus reducing the compressive stresses acting in the contact zone.
Frictional losses and lubrication Since the piston orbits but does not rotate, all positions on the piston describe a circle whose radius is the throw of the crank. Consequently, rubbing speeds are much lower than in rotary engines where the piston also rotates, such as the Wankel engine. These low rubbing speeds lead to low frictional losses of power. There appear to be no lubrication problems unique to the orbital displacer where pressurized oil systems can be used. Since “crankcase compression” is not used in the orbital two-stroke engines cited above, a total loss oil system (with its “sooty” exhaust) is not required.
32
Positive Displacement Machines
Combustion in orbital displacers Although it is difficult to design an orbital displacer where the ratio of the surface area of the working cavity to the displacement is as low as that of a reciprocating internal combustion engine, this ratio will generally be much lower than that pertaining to the Wankel engine. Note that the centre of the working volume moves in a roughly elliptical orbit, whereas it moves straight up and down in a reciprocating engine. This should cause an inherent swirl of the fuel/air mixture which could be used to facilitate combustion. See Fig. 31. Furthermore, if the clearance between the crown of the piston and the housing is minimized, a very high gas velocity across the piston crown can be achieved. Just before TDC most of the working volume is located adjacent to the leading vane. Just after TDC most of the working volume is located adjacent to the trailing vane. See Fig. 32. If a shallow groove in the piston crown links the leading vane pad to the trailing vain pad, most of the fuel/air mixture will be forced to flow through this groove around TDC. If one or more spark plugs were located in the housing above this groove, all the fuel/
Fig. 31 Schematic of swirl in orbital power chamber.
Fig. 32 Squish in orbital power chamber.
The orbital displacer: Implications and applications
33
air mixture could be squirted past these discharging spark plugs around TDC—thus making the combustion process less dependent on the rate of flame propagation.
Cooling of orbital engines In the (single rotor) Wankel engine, the combustion chambers travel past a single inlet port, single sparkplug and single exhaust port. In this case, the heat flow to the housing is nonuniform, thus complicating the thermal expansion and cooling problems. In an orbital engine, the combustion chambers tend to be uniformly distributed around the axis of their crankshaft. In general, if there are N vanes there will be N combustion chambers, each with its own sparkplug and inlet and exhaust ports. In this case, the heat flow to the housing should show radial symmetry, thus simplifying the thermal expansion and cooling problems. Since the orbiting piston will generally float between the end plates and does not touch the housing, its cooling is a potential problem. A similar problem occurs in the Wankel engine. Forced convection will be required to cool the orbiting piston. In small engines air circulation may suffice, whereas in larger engines oil cooling of the piston may be required. Cooling holes could be drilled through the piston parallel to the axes of the eccentrics, which intermittently align with cooling holes in the end plates. Air could be drawn through these holes by a fan attached to one or more of the eccentrics. Alternatively, oil could be pumped through much smaller holes through the orbiting piston.
Manufacturing processes and materials In theory, the cost of manufacturing an orbital displacer could be less than that pertaining to a reciprocating displacer. First, with the exception of the sealing elements, there are fewer components required—especially in the case of orbital pumps and motors, where valveless port timing can be used to eliminate the need for valves. Furthermore, little machining is required. In the external housing or internal core, only the vane slots and end faces need to be machined. On the end plates, only the inner faces, the grooves for the vanes, and the bores for the crankshaft need to be machined. On the piston, only the end faces, the pads for the vanes, and the eccentric bore need to be machined. Most
34
Positive Displacement Machines
surfaces of the vanes will need to be machined, as will the crankshaft eccentric and stabilizing plate. The 6 cc model aircraft engine was designed to be manufactured from an Al-17% Si alloy which combines lightness with wear resistance.
Conclusions The orbital displacer originally conceived by Ralph Sarich may have greater significance than its application as a four-stroke internal combustion engine. Although the automobile engine market is very large, it is also the hardest to penetrate due to the high degree of sophistication of the design and manufacture of reciprocating engines and the large number of often conflicting requirements that must be satisfied. It may be more rewarding to first penetrate a smaller, less competitive market and then use this as a base from which to expand into larger more difficult markets. Asymmetric port timing comes naturally to orbital displacers. This valveless port timing can be used to advantage in orbital two-stroke engines, hydraulic pumps and motors, pneumatic compressors and motors, and Rankine engines. Engineering students have found orbital displacer projects stimulating in the originality required, as they generally had to go back to first principles to solve problems.
Acknowledgements The authors would like to thank the staff and students of the Gippsland School of Engineering (now part of Federation University Australia) for their contribution to this paper.
References Hancorne, J. A. (1979). Student project report. Gippsland Institute of Advanced Education. Private Communication. Sarich, T. R. (1970). An improved rotary motor. Australian patent 467415, filing date 6 July 1970. Sarich, T. R. (1973). Improved vane type internal combustion engines. Australian patent 477125, filing date 16 January 1973. Sarich, T. R. (1974). Gas seal for vane type internal combustion engine. (US patent 3938916, filing date 16 January 1974). Sarich, T. R. (1975). Improved orbital engine with stabilising plate. In Australian patent 491267, filing date 3 February 1975. Sarich, T. R. (1976a). Orbital engine with stabilizing plate. US patent 4037997, filing date 3 February 1976a.
The orbital displacer: Implications and applications
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Sarich, T. R. (1976b). Vane type orbital engine. US patent 4079083, filing date 3 February 1976b. Spark, I. J., Rossin, J. M., & Sincich, R. (1973a). Improved orbital displacers. Australian patent 487540, filing date 2 July 1973. Spark, I. J., Rossin, J. M., & Sincich, R. (1973b). Orbital displacer. US patent 487540, filing date 2 July 1973. Spark, I. J., Rossin, J. M., & Sincich, R. (1973c). Improvements in rotary positive-displacement machines. UK patent 1480137, filing date 2 July 1973. Spark, I. J., Rossin, J. M., & Sincich, R. (1973d). Orbital displacers. Canadian patent 1043267, filing date 2 July 1973. Wankel, F. (1963). Rotary piston machines. London: Iliffe Books.